Documentation

Foundation.FirstOrder.Basic.Coding

def LO.FirstOrder.Semiterm.toNat {L : Language} [(k : ) → Encodable (L.Func k)] {ξ : Type u_1} [Encodable ξ] {n : } :
Semiterm L ξ n
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    @[irreducible]
    def LO.FirstOrder.Semiterm.ofNat {L : Language} [(k : ) → Encodable (L.Func k)] {ξ : Type u_1} [Encodable ξ] (n a✝ : ) :
    Option (Semiterm L ξ n)
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      theorem LO.FirstOrder.Semiterm.ofNat_toNat {L : Language} [(k : ) → Encodable (L.Func k)] {ξ : Type u_1} [Encodable ξ] {n : } (t : Semiterm L ξ n) :
      ofNat n t.toNat = some t
      instance LO.FirstOrder.Semiterm.encodable {L : Language} [(k : ) → Encodable (L.Func k)] {ξ : Type u_1} [Encodable ξ] {n : } :
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      def LO.FirstOrder.Semiformula.toNat {L : Language} [(k : ) → Encodable (L.Func k)] {ξ : Type u_1} [Encodable ξ] [(k : ) → Encodable (L.Rel k)] {n : } :
      Semiformula L ξ n
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        @[irreducible]
        def LO.FirstOrder.Semiformula.ofNat {L : Language} [(k : ) → Encodable (L.Func k)] {ξ : Type u_1} [Encodable ξ] [(k : ) → Encodable (L.Rel k)] (n a✝ : ) :
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          theorem LO.FirstOrder.Semiformula.ofNat_toNat {L : Language} [(k : ) → Encodable (L.Func k)] {ξ : Type u_1} [Encodable ξ] [(k : ) → Encodable (L.Rel k)] {n : } (φ : Semiformula L ξ n) :
          ofNat n φ.toNat = some φ
          instance LO.FirstOrder.Semiformula.encodable {L : Language} [(k : ) → Encodable (L.Func k)] {ξ : Type u_1} [Encodable ξ] [(k : ) → Encodable (L.Rel k)] {n : } :
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